Ofcourse, otherwise you wouldn't be able to call yourself a true Pokémon Master. I have heard of some people who release their partners just because they don't have the right nature or ability! Those people aren't trainers, they are the monsters!
There can only be one, like in that foreign movie where there could only be one, and in the end there is only one dude left, because that was the point. - Kenji
I'm always sentimental for my in-game team; it's one of the reasons why I like to finish it as early as possible, preferbly by 5th Gym latest. So that by end-game, I can see just how much they've grown and how long we've been together.
Action speaks louder than words. But words, when used right, overwhelm any action - Me, 2006 Let's put a smile on that face - The Joker, 2008
You are sentimental about you work/time/effort you put into the game, not about the actual Pokemon themselves.
Build a ship model from 10000 pieces, collect 700 Pokemon and raise them all, collect thousands of post stamps. Doesn't matter. If someone destroys the collection you will be angry. You don't miss the actual object/collection/data, you are only angry because you surely wasted your time when your collection is destroyed.
Go ask a neuro-scientist about it, he will agree, because he studied it and did the measurements.